Algebra
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Axioms of Algebra
An Axiom is a mathematical statement that is assumed to be true. There are five basic axioms of algebra. The axioms are the reflexive axiom, symmetric axiom, transitive axiom, additive axiom and multiplicative axiom.
- Reflexive Axiom: A number is equal to itelf. (e.g a = a). This is the first axiom of equality. It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."
- Symmetric Axiom: Numbers are symmetric around the equals sign. If a = b then b = a. This is the second axiom of equality It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."
- Transitive Axiom: If a = b and b = c then a = c. This is the third axiom of equality. It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."
- Additive Axiom: If a = b and c = d then a + c = b + d. If two quantities are equal and an equal amount is added to each, they are still equal.
- Multiplicative Axiom: If a=b and c = d then ac = bd. Since multiplication is just repeated addition, the multiplicative axiom follows from the additive axiom.
